I may have misunderstood the question, in which case downvote me and tell me so.
As I understand it, you're asking how to tell the difference between these:
Residents asked for opinions on their neighborhood.
Residents asked for opinions on their neighborhood had little to say.
So, you're asking how to tell if the resident is doing the asking, or is being asked.
I could be wrong, but I don't think it's possible for this to be ambiguous. I cannot think of any examples.
You can tell the difference by looking for a second verb.
If the residents are asking questions, the residents will have only one verb attached to them:
Residents asked what the police were doing.
^In that example the second verb were doing belongs to the police, not the residents. If you understand the usage of what in this sentence, it's not possible to confuse this with the second structure.
Now, if that had been the second structure, where someone is asking the residents, the previous example would be grammatically incorrect, and not a sentence. Let's look at it again.
Residents asked what the police were doing.
You see, if the residents were being asked, this would mean nothing. It would serve as a subject clause for a longer sentence, but would mean nothing by itself because it has no other verb. Which residents? The residents who were asked questions. What did they do? I don't know, the "sentence" didn't say.
Remember that a sentence must have both a subject and a verb! If "the residents who were asked questions" are the subjects, what is the verb? Answer: there is none, because this isn't a sentence if the residents are the ones being asked!
Right: Residents asked what the police were doing said they didn't know.
Wrong: Residents asked what the police were doing.... and what? Nothing! This is a fragment, so it cannot be the second structure. In this sentence, the residents must be the ones doing the asking.
There is the final possibility, as WendiKidd points out, that the sentence merely seeks to declare that the residents were asked questions. In that case, you cannot just say asked, you must say were asked.
The residents were asked questions.